Phase Structure of Internal Gravity Waves in the Ocean with Shear Flows

Purpose. The description of the internal gravity waves dynamics in the ocean with background fields of shear currents is a very difficult problem even in the linear approximation. The mathematical problem describing wave dynamics is reduced to the analysis of a system of partial differential equations; and while taking into account the vertical and horizontal inhomogeneity, this system of equations does not allow separation of the variables. Application of various approximations makes it possible to construct analytical solutions for the model distributions of buoyancy frequency and background shear ocean currents. The work is aimed at studying dynamics of internal gravity waves in the ocean with the arbitrary and model distributions of density and background shear currents. Methods and Results. The paper represents the numerical and analytical solutions describing the main phase characteristics of the internal gravity wave fields in the stratified ocean of finite depth, both for arbitrary and model distributions of the buoyancy frequency and the background shear currents. The currents are considered to be stationary and horizontally homogeneous on the assumption that the scale of the currents' horizontal and temporal variability is much larger than the characteristic lengths and periods of internal gravity waves. Having been used, the Fourier method permitted to obtain integral representations of the solutions under the Miles – Howard stability condition is fulfilled. To solve the vertical spectral problem, proposed is the algorithm for calculating the main dispersion dependences that determine the phase characteristics of the generated wave fields. The calculations for one real distribution of buoyancy frequency and shear flow profile are represented. Transformation of the dispersion surfaces and phase structures of the internal gravitational waves’ fields is studied depending on the generation parameters. To solve the problem analytically, constant distribution of the buoyancy frequency and linear dependences of the background shear current on depth were used. For the model distribution of the buoyancy and shear flow frequencies, the explicit analytical expressions describing the solutions of the vertical spectral problem were derived. The numerical and asymptotic solutions for the characteristic oceanic parameters were compared. Conclusions. The obtained results show that the asymptotic constructions using the model dependences of the buoyancy frequency and the background shear velocities’ distribution, describe the numerical solutions of the vertical spectral problem to a good degree of accuracy. The model representations, having been applied for hydrological parameters, make it possible to describe qualitatively correctly the main characteristics of internal gravity waves in the ocean with the arbitrary background shear currents.

Vertical Transfer of Momentum by Inertia-Gravity Internal Waves on a Two-Dimensional Shear Flow

Purpose. The paper is aimed at investigating the momentum vertical transfer by inertia-gravity internal waves on a two-dimensional flow with a vertical shear of velocity, and also at studying the Stokes drift of liquid particles and the mean current effect on it. Methods and Results. Free internal waves in an infinite basin of constant depth are considered in the Boussinesq approximation with the regard for the Earth rotation. Two components of the mean current velocity depend on the vertical coordinate. The equation for the vertical velocity amplitude has complex coefficients; therefore the eigenfunction and the wave frequency are complex. The corresponding boundary value problem is solved numerically by the implicit Adams scheme of the third order of accuracy. The wave frequency at a fixed wavenumber was found by the shooting method. It was determined that the frequency imaginary part was small and could be either negative or positive depending on a wave number and a mode number. Thus, both weak attenuation and weak amplification of an internal wave are possible. The vertical wave momentum fluxes are nonzero and can exceed the corresponding turbulent fluxes. The Stokes drift velocity, transverse to the wave direction, is nonzero and less than the longitudinal velocity. The vertical component of the Stokes drift velocity is also nonzero and four orders of magnitude less than the longitudinal component. The signs of the vertical component of the Stokes drift velocity for the waves with the frequencies 10 and 16 cycle/h are opposite, since the signs of their frequency imaginary parts are different; and the vertical component of the Stokes drift velocity is proportional to the wave frequency imaginary part. Conclusions. The vertical momentum wave flux of inertia-gravity internal waves differs from zero in the presence of the current whose velocity component, transverse to the wave propagation direction, depends on the vertical coordinate. The component of the Stokes drift velocity, transverse to the wave propagation direction, is nonzero and less than the longitudinal one. The vertical component of the Stokes drift velocity is also nonzero and can contribute to formation of the vertical fine structure

Skewness and Kurtosis of the Surface Wave in the Coastal Zone of the Black Sea

Purpose. The aim of the study is to analyze variability of the statistical moments characterizing deviations of the sea surface elevation distributions from the Gaussian one. Methods and Results. Field studies of the sea waves’ characteristics were carried out from the stationary oceanographic platform located in the Black Sea near the Southern coast of Crimea. The data obtained both in summer and winter, were used. The statistical moments were calculated separately for wind waves and swell. The measurements were performed in a wide range of meteorological conditions and wave parameters (wind speed varied from 0 to 26 m/s, wave age – from 0 to 5.2 and steepness – from 0.005 to 0.095). For wind waves, the coefficients of skewness correlation with the waves’ steepness and age were equal to 0.46 and 0.38. The kurtosis correlation coefficients with these parameters were small (0.09 and 0.07), but with the confidence level 99.8% – significant. For swell, the correlation coefficients were 1.5 – 2.0 times lower. Conclusions. The statistical moments of the sea surface elevations of the third and higher orders are the indicators of the wave field nonlinearity, which should be taken into account when solving a wide range of the applied and fundamental problems. The deviations of the surface elevation distributions from the Gaussian one are not described unambiguously by the waves’ steepness and age. At the fixed values of these parameters, a large scatter in the values of the surface elevations’ asymmetry and kurtosis is observed. This imposes significant limitations on the possibility of applying the nonlinear wave models based on the wave profile expansion by small parameter (steepness) degrees, in engineering calculations.

Assessment of the Black Sea Temperature and Salinity Climatic Fields for the Recent Climatological Period (1991–2020)

Purpose. The study is aimed at assessing a new climatic array of the Black Sea temperature and salinity calculated using hydrological observations for the standard (according to the World Meteorological Organization definition) 30-year climatological period 1991–2020. Methods and Results. New array of the temperature and salinity climatic fields was assessed based on analyzing the results of numerical experiments. In the experiment, annual variation of the Black Sea hydrophysical parameters was reproduced by the numerical model. Modeling included the scheme of assimilating the data of the climatic temperature and salinity array assessed. In contrast to the averaged data of the field observations, the model fields were matched from the viewpoint of the motion equations. Besides the temperature and salinity three-dimensional fields, the three-dimensional climatic fields of the Black Sea currents were also reproduced for each day of a climatic year that is quite impossible using the instrumental measurements data only. Spatial-temporal variability of the modeled three-dimensional fields was analyzed. The integral characteristics of the Black Sea water dynamics for the recent 30-year climatic period were studied and compared with the analogous ones for the previous century. Simulation was performed at the grid with the 5 km horizontal resolution using the EMODNet bathymetry by means of the three-dimensional non-linear model of the Black Sea dynamics developed in Marine Hydrophysical Institute. Having been analyzed, the performed calculations showed that the increased spatial resolution of the temperature and salinity climatic array for the recent period made it possible to reproduce dynamics in all the layers of the Black Sea waters in more details. At the same time, a significant small-scale variability, most pronounced at the deep-water horizons, was present in the salinity fields. Conclusions. As compared to the experiment with assimilation of the previous version of the climatic array, the modeling based on the new array of the thermohaline fields revealed increase in the integral temperature of the upper mixed layer. At that, thinning and «break» of the cold intermediate layer found in the central part of the sea, indicates warming of the sea upper layer during the last 30 years. The highest noisiness detected at the deep-water horizons in the modeled salinity fields is related to quantity and quality of the salinity data resulted from the field observations. Taking into account insufficient metrological facilities for measuring seawater electrical conductivity, the next version of climatic array requires a more strict procedure for verifying and processing the observation data obtained in the deep-sea layers.

Features of Currents on the Black Sea Northwestern Shelf Based on the Numerical Simulation Results

Purpose. The work is aimed at studying the features of currents on the Black Sea northwestern shelf based of the reanalysis results, and at analyzing the reasons of these features. Methods and Results. To analyze the currents on the northwestern shelf, applied were the results of physical reanalysis of the Black Sea fields performed by the authors earlier, namely, the arrays of hydrodynamic fields on a regular grid with the 21-year duration (1992–2012). Surface currents on the northwestern shelf of the Black Sea are directed mainly to the southwest. Throughout the whole year (except for the summer months when the wind effect weakens), an intensive compensatory current directed to the south is formed along the western coast. The waters near the western coast are highly horizontally stratified that is caused by fresh water inflowing with the river runoffs. In winter seasons, the stratification is most pronounced, whereas in summer, the horizontal density gradient decreases. The horizontal density stratification leads to the following: starting from the depth ~ 20 m, the pressure gradient changes its sign and the along-coastal jet countercurrent directed to the north, occurs. Conclusions. The performed studies have shown that the water circulation on the Black Sea northwestern shelf is determined mainly by the following factors: the wind-induced water flows across the shelf boundary and strong horizontal water stratification near the western coast resulted from the river runoffs. As the currents on the sea surface are directed mainly to the southwest, the compensatory current directed to the south is formed near the western coast. Due to the strong horizontal stratification resulted from the river runoffs, a countercurrent directed to the north is formed in the subsurface layer near the western coast. In case the seawater flows to the shelf are extremely high, the countercurrent may be absent.

Basic Regularities of Vertical Turbulent Exchange in the Mixed and Stratified Layers of the Black Sea

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. For the upper mixed layer, the turbulent energy dissipation rate ɛ and the exchange coefficient were calculated using the velocity fluctuation spectra based on the Kolmogorov hypotheses on the turbulence spectrum inertial range. In the stratified layers, the turbulence coefficient and the dissipation rate were experimentally determined both from the spectra of the velocity horizontal fluctuations’ gradients and the vertical spectra of temperature fluctuations using the concept of the effective scale of turbulent spots. Depending on the features of the hydrological regime and the prevailing energy contributors to turbulence generation, five layers were identified and described (including their characteristic power dependences of the vertical turbulent diffusion coefficients K on the buoyancy frequency N) using the 1.5D-model of vertical turbulent exchange for the basin under study. For the stratified layers, the 1.5D-model results were comparatively analyzed with those of the other semi-empirical and theoretical models describing the most probable hydrophysical processes in each specific layer; the relations for the vertical turbulent exchange coefficient were obtained depending on the buoyancy frequency. Conclusions. Comparison of the experimental data collected under different hydrometeorological conditions with the simulations resulted from the known turbulence models for the sea upper layer showed that the best agreement between the simulation and measurement data was provided by a multiscale model taking into account three basic mechanisms of turbulence generation: current velocity shear, instability of wave motions, and wave breaking. The turbulent exchange coefficient dependencies on depth are conditioned by the affect of the turbulence dominant source at a given level. In the stratified layers, the exchange coefficient dependence on buoyancy frequency is determined by the hydrophysical processes in each layer; the relations obtained for individual layers indicate intensity of the contributions of vertical advection, internal wave breakings, turbulence diffusion and geothermal flux.

Spatial Characteristics of the Black Sea Cold Intermediate Layer in Summer, 2017

Purpose. The aim of the paper is to study spatial characteristics of the cold intermediate layer (CIL) after its waters were renewed due to the cold winter, using analysis of the data obtained during the Black Sea expedition in June 14 – July 3, 2017 (the 95th cruise of R/V “Professor Vodyanitsky”). Methods and Results. The data both from the CTD-measurements by the SBE911+ probe and the current velocity profile measurements by the Lowered Acoustic Doppler Current Profiler (LADCP) were used. Isopycnic averaging of the profile ensembles was applied to obtain the averaged characteristics of the water vertical thermohaline structure. During the measurement period, the minimum average temperature of the CIL core was 7.2°C at the density value 14.5 kg/m3 . The layer upper boundary (according to the 8°C criterion) corresponded to the density value 14.3 kg/m3 , its lower one – to 15.0 kg/m3 . CIL water formation was most pronounced in the vicinity of the Rim Current, which was clearly seen on the isopycnic surfaces 14.6, and 15.0 kg/m3 . According to the measurements, the main mass of CIL waters was identified in the Rim Current and in its right part (on the coast side). The CIL maximum thickness was 60 m and the vertical position of its core corresponded to the 40–100 m depth. Conclusions. The synchronous profiles of current velocity, temperature, salinity, and density obtained in the Black Sea expedition in summer, 2017 made it possible to analyze the waters thermohaline structure with the regard for real dynamic situation. As a result, the CIL parameters, its spatial scales and position relative to the Rim Current were determined with due regard for the features of the density field structure in summer, 2017. This information can be useful for model verification and numerical experiments aimed at studying the mechanisms and the areas of CIL formation in the Black Sea

Evaluation of GPM IMERG Products and Estimation of Warm-Season Precipitation in Crimea

Purpose. The study was aimed at the evaluation of the Integrated MultisatellitE Retrievals from GPM (IMERG) remote sensing dataset using ground observations and estimation of the 2006–2018 warmseason precipitation in the Crimean Peninsula. Methods and Results. Evaluation of the IMERG dataset was performed using the meteorological station observations treated as the ground truth. We provided the multiyear statistical characteristics of precipitation amounts, frequency and intensity for different climate zones of the Crimean Peninsula. We considered the spatial variability of summer precipitation, bias and correlation between IMERG and the ground observations. Conclusions. IMERG has a weaker spatial variability compared to the ground observations. The warm-season IMERG bias is small in the central and mountainous parts of Crimea, whereas the precipitation estimates in the coastal zones are substantially overestimated. The IMERG wet bias is mostly caused by the excessive rainfall frequency. The temporal variability of IMERG is in good agreement with the observations with an average correlation coefficient 0.73. For most of the metrics considered, warm-season IMERG precipitation significantly outperforms the other datasets in the central and mountainous parts of Crimea and could be used for practical tasks with certain precautions. At the same time, due to the lack of calibration over the marine areas, the quality of IMERG precipitation estimates in the coastal zones is reduced.

Model and Experimental Estimates of Vertical Mixing Intensity in the Sea Upper Homogeneous Layer

Purpose. The study is aimed at qualitative and quantitative analysis (based on the updated previously proposed multiscale model) of the experimental data on turbulence intensity and their comparison with theoretical and semi-empirical relationships for the purpose of describing the contributions of various turbulence sources. Methods and Results. A comparative analysis of experimental data and model calculations of turbulence characteristics near the sea surface was performed. The methods of theoretical assessing generation of turbulence in the near-surface sea layer by various physical processes are considered. The results of calculations by the well-known models of turbulent exchange were compared with the experimental data collected by the scientists of the Turbulence Department of MHI, RAS, using the specialized equipment. The analysis results made it possible to determine the possibility of applying the considered models for calculating turbulence intensity under different hydrometeorological conditions. At light winds, none of the models yielded the results which matched the measurement data. At moderate winds, the simulation results showed quite satisfactory agreement with the experiment data; and for strong winds, the multiscale model results were the best. This model was modified to assess the contributions of two other mechanisms of turbulence generation: the Stokes drift and the Langmuir circulations. Conclusions. Objective assessment of the turbulent exchange intensity requires taking into account of three main mechanisms of turbulence generation, namely flow velocity shear, wave motions and wave breaking. Depending on the hydrometeorological situation, each of these mechanisms can dominate in a certain depth range. The calculations performed using the updated model showed that the Stokes drift added 2–17 % to the total dissipation in the upper 30-meter layer, whereas the contribution of the Langmuir circulations calculated through dependence of the vertical velocity of kinetic energy transfer upon the Langmuir number, can reach 15 % for small Langmuir numbers.

Study of the Mechanisms of Vortex Variability in the Lofoten Basin Based on the Energy Analysis

Purpose. The Lofoten Basin is one of the most energetic zones of the World Ocean characterized by high activity of mesoscale eddies. The study is aimed at analyzing different components of general energy in the basin, namely the mean kinetic and vortex kinetic energy calculated using the integral of the volume of available potential and kinetic energy of the Lofoten Vortex, as well as variability of these characteristics. Methods and Results. GLORYS12V1 reanalysis data for the period 2010–2018 were used. The mean kinetic energy and the eddy kinetic one were analyzed; and as for the Lofoten Vortex, its volume available potential and kinetic energy were studied. The mesoscale activity of eddies in winter is higher than in summer. Evolution of the available potential energy and kinetic energy of the Lofoten Vortex up to the 1000 m horizon was studied. It is shown that the vortex available potential energy exceeds the kinetic one by an order of magnitude, and there is a positive trend with the coefficient 0,23⋅1015 J/year. It was found that in the Lofoten Basin, the intermediate layer from 600 to 900 m made the largest contribution to the potential energy, whereas the 0–400 m layer – to kinetic energy. The conversion rates of the mean kinetic energy into the vortex kinetic one and the mean available potential energy into the vortex available potential one (barotropic and baroclinic instability) were analyzed. It is shown that the first type of transformation dominates in summer, while the second one is characterized by its increase in winter. Conclusions. The vertical profile shows that the kinetic energy of eddies in winter is higher than in summer. The available potential energy of a vortex is by an order of magnitude greater than the kinetic energy. An increase in the available potential energy is confirmed by a significant positive trend and by a decrease in the vortex Burger number. The graphs of the barotropic instability conversion rate demonstrate the multidirectional flows in the vortex zone with the dipole structure observed in a winter period, and the tripole one – in summer. The barotropic instability highest intensity is observed in summer. The baroclinic instability is characterized by intensification of the regime in winter that is associated with weakening of stratification in this period owing to winter convection.